But Sauron used Elvish runes to write his message on the One Ring, according to Gandfalf: Elvish letters using the language of Mordor (The Shadow of the Past.) We could say that's inconsistent too, but I'd say there's a lot of complexity in Middle-earth, and to qualify every statement used in dialogue or description would be unwieldy, so I don't take Tolkien's declarations at face value unless there's a compelling reason to. I take the point in the dialogue to mean that the other two are correcting Gimli's perception that if you see an "S" on orc armor, it means Sauron. Tolkien is trying to deepen the mystery a little here for these three on who their real enemy is.

‘S is for Sauron,’ said Gimli. ‘That is easy to read.’ ‘Nay!’ said Legolas. ‘Sauron does not use the Elf-runes. Except when he is writing on Rings of Power messages that only he will read." ‘Neither does he use his right name, nor permit it to be spelt or spoken, except by his messengers and spokespersons in certain diplomatic situations, or when they've been foiled from seizing the ring in hobbit homes in Buckland, or when...,’ said Aragorn.